Traveling-waves in DC-biased metallic carbon nanotubes: Theoretical investigation of amplification and fabrication of characterization fixture .

摘要

Radio-frequency (RF) generation and amplification is at the heart of telecommunication, satellite and optoelectronics applications. The electronics industry is in constant search for RF amplifiers that are smaller, more efficient, and operating at higher frequencies. Nanomaterials with unique properties promise to fulfill these characteristics while bridging the gap between vacuum-based and solid-state amplifiers. In this thesis, we specifically investigate the capability of carbon nanotubes (CNTs) in amplification of traveling-waves at RF frequencies. Using theoretical means, we show that such amplification is indeed a possibility. We also design and fabricate the characterization fixture needed for measurements and testing the theory.;Over the last two decades, CNTs have proved that they possess remarkable electrical properties. Two of these properties incite the following study. First, CNTs possess a large electron drift velocity due to their long mean free path at room temperature. Furthermore, electromagnetic surface-wave propagation along a CNT acquires a large slow-wave factor due to the smallness of the radius and the infinitesimal wall thickness. The drift and phase velocities are calculated to be on the same order of magnitude, thereby immensely motivating this study : such synchronization between the electrons and the RF field is exactly the physical mechanism used in traveling-wave tubes (TWTs) to induce amplification.;In general, the theoretical problem is to investigate the outcome of applying simultaneous DC and RF fields across a metallic-CNT. For this purpose, the CNT current density is first calculated through a semi-classical transport problem. Then, through coupling with the electromagnetic problem, an eigenmode solution is reached. Finally, RF traveling-wave amplification is found above a certain threshold DC field.;Particularly, from the particle's transport perspective, we use the Boltzmann transport equation (BTE) to calculate the distribution of the charge carriers under DC and AC fields. Afterwards, the Boltzmann AC current density is found with respect to the applied DC field. Negative differential conductivity (NDC) is found under moderate fields. By approximating the electronic dispersion of CNTs as a linear function, we find analytical solutions for the distribution and current density that agree reasonably well with the full-band numerical solution of the differential equations.;From the electromagnetic wave perspective, we use Maxwell's equations to find the solution for surface-wave propagation along a hollow conductor which is the CNT. Using the surface boundary conditions, we reach a relation for the Maxwell current density. By equating the currents calculated through the transport and electromagnetic aspects at all points in space-time, we find a determinantal equation whose solution is the electromagnetic dispersion.;In the absence of a DC field, the immense slow-wave factor in CNTs is attributed largely to the geometry of the problem. On the other hand, the RF propagation is found to be largely modulated by the application and subsequent increase of a DC field.;Assuming negligible spatial dispersion, an amplification was found beyond a threshold value of 3 x 105 V/m, as signalled by a positive attenuation factor. At such fields, the amplification response is explained in our model through Bloch-type reflections at the Brillouin zone (BZ) edges, instead of the expected TWT-like behavior.;However, preliminary calculations that included the spatial dispersion lead to the appearance of an amplified mode at a lower field of 10 4 V/m. Interestingly, the phase and drift velocities are matched at this field magnitude, which suggests a possibility of a TWT-like amplification. However crude, these results point to the importance of the previously neglected non-local effects, which are worthy of a more rigorous calculation that makes use of complex plane analysis techniques.;Due to technical shortcomings, the experimental aim of the work was limited to the design and fabrication of the RF characterization fixture which could later be used to investigate the problem experimentally. The coplanar waveguide (CPW) was the planar waveguide of choice thanks to its versatility and high-frequency capabilities. The CPW signal trace was tapered and a gap opening allowed for CNTs, ideally one, to be aligned for measurements. The CNTs were deposited on the substrates using spin-coating as a first step. Then, using the atomic force microscope (AFM), the deposition was refined to the desired concentration and alignment. Afterwards, the CPW electrodes were patterned using standard optical lithography/lift-off. After this final step, alignment across the CPW gaps was probed using the scanning electron microscope (SEM). As a result, we found numerous CPWs contacted by a single or multiple CNTs