Francisco R. Madriz

Circuit Modeling of High-Frequency Electrical Conduction in Carbon Nanofibers

We show that the simplest possible circuit model of high-frequency electrical conduction in carbon nanofibers from 0.1 to 50 GHz is a frequency-independent resistor in parallel with a frequency-independent capacitor. The resistance is experimentally determined and represents the total dc resistance of the nanofiber and its contacts with the electrodes. The capacitance is obtained as a free parameter and has not been previously observed. The experimental method utilizes a ground-signal-ground test structure whose two-port scattering parameters (S-parameters) can be described to within plusmn0.5 dB and plusmn2deg using a simple lumped-element circuit model. The nanostructure is placed in the signal path of the test structure, and its equivalent circuit is deduced by determining what additional elements must be added to the test structure circuit model to reproduce the resulting changes in the S-parameters. This methodology is applicable to nanowires and nanotubes.

Inductance in One-Dimensional Nanostructures

The physical origin of kinetic inductance is examined for 1-D nanostructures, where the Fermi liquid theory prevails. In order to have appreciable kinetic inductance, ballistic transport must exist, with no inelastic scattering inside the nanowires. Kinetic inductance is assigned to the nanowire itself and independent of its surroundings, whereas magnetic inductance is assigned to the nanowire and substrate. Kinetic and magnetic inductances are in series in an equivalent circuit representation. If there are m transmission modes and n multiwalls in the nanostructure, kinetic inductance decreases by a factor of 1/(mn). The relation of the predicted results to preliminary experimental findings is discussed.

Thermoreflectance Measurement of Temperature and Thermal Resistance of Thin Film Gold

To improve performance and reliability of integrated circuits, accurate knowledge of thermal transport properties must be possessed. In particular, reduced dimensions increase boundary scattering and the significance of thermal contact resistance. A thermoreflectance measurement can be used with a valid heat transport model to experimentally quantify the contact thermal resistance of thin film interconnects. In the current work, a quasi-steady state thermoreflectance measurement is used to determine the temperature distribution of a thin film gold interconnect (100 nm) undergoing Joule heating. By comparing the data to a heat transport model accounting for thermal diffusion, dissipation, and Joule heating, a measure of the thermal dissipation or overall thermal resistance of unit area is obtained. The gold film to substrate overall thermal resistance of unit area beneath the wide lead (10 μm) and narrow line (1 μm) of the interconnect are 1.64 × 10−6 m2 K/W and 5.94 × 10−6 m2 K/W, respectively. The thermal resistance of unit area measurements is comparable with published results based on a pump-probe thermoreflectance measurement.

Frequency-Independent

We demonstrate that a frequency-independent parallel RC circuit is the simplest model that accurately describes high-frequency electrical conduction in 1-D nanostructures. The resistance is determined from dc measurement, and the capacitance is extracted directly from the measured S-parameters for a ground-signal-ground test structure, without using any fitting parameter. The methodology is applied to carbon nanofibers, and the RC model yields results that are within ±0.5 dB and ±5° of the measured S-parameters up to 50 GHz. The model is further justified by examining the relationship between S- and Y-parameters of the test network.

RC

We study electrical conduction in carbon nanofibers from 0.1 to 30 GHz, by measuring the S-parameters of a ground-signal-ground test structure in which a nanofiber forms part of the signal path. If the nanofiber is modeled as a resistor, the S-parameters are reproduced well by a simple, but realistic, lumped RC circuit model. This implies that, as at low frequencies, nanofibers behave as resistors all the way up to microwave frequencies.

Circuit Model for One-Dimensional Carbon Nanostructures

We describe a test structure optimized for studying high-frequency electrical transport in 1-D nanoscale systems. The test structure exhibits lower transmission than previously reported structures, enabling capacitances less than 1 fF to be detected in the frequency response of the nanoscale system. The scattering parameters (S-parameters) of the test structure are describable to within ±0.5dB and ±2° from 0.1 to 50 GHz using a simple lumped-element RC circuit model whose elements are all measured experimentally.

Measurements and Circuit Model of Carbon Nanofibers at Microwave Frequencies

Carbon nanotubes (CNTs) and carbon nanofibers (CNFs) are potential materials for the most advanced silicon devices and circuits due to their excellent electrical properties such as high current capacity and tolerance to electromigration. In addition, at high frequencies, these materials exhibit transport behavior which holds promise for applications as on-chip interconnects.

Test Structure to Extract Circuit Models of Nanostructures Operating at High Frequencies

Based on extensive measurements and analysis, we establish that a frequency-independent parallel AC circuit can accurately model the high-frequency electrical conduction in 1-D nanostructures. The methodology is applied to carbon nanofibers and the AC model yields results that are within ± 0.5 dB and ± 5° of measured 5-parameters up to 50 GHz.