Nano-scale electrical contacts are essential for next generation electronics. Based on the materials of the contact members and the interfacial layers, these junctions can be of ohmic, Schottky or tunneling type. Nonuniform current distribution and current crowding across electrical contacts lead to nonuniform heat deposition, formation of local thermal hotspots, aggravation of electromigration, and in the worst scenario, lead to thermal runaway and breakdown of the device. Contact resistance, on the other hand, severely restricts the current flow, and affects the overall device properties. Devices based on thin film junctions, nanotubes or nanowires, and two-dimensional (2D) materials are especially sensitive to the current transport at electrical contacts, due to their reduced dimensions and increased geometrical confinement for the current flow. The goal of this thesis is to develop theoretical models to understand, improve, and control current transport and to reduce contact resistance in nanoscale electrical contacts.First, we study the current density-voltage (J-V) characteristics of dissimilar metal-insulator-metal (MIM) nanoscale tunneling junctions using a self-consistent quantum model. Tunneling type contacts are ubiquitous as they can be formed when a thin insulator layer or gap exists between two contacting members. Our model includes electron emissions from both the cathode and anode, and the effects of image charge potential, space charge and exchange correlation potential. The J-V curves span three regimes: direct tunneling, field emission, and space-charge-limited regime. Unlike similar MIM junctions, the J-V curves are polarity dependent. The forward and reverse bias J-V curves and their crossover behaviors are examined in detail for various regimes, over a wide range of material properties. It is found that the asymmetry between the current density profiles increases with the work function difference between the electrodes, insulator layer thickness, and relative permittivity of the insulator. This asymmetry is profound in the field emission regime and is insignificant in the direct tunneling, and space charge limited regimes. Next, we study the current distribution and contact resistance in ohmic, tunneling and two-dimensional (2D) material-based Schottky contacts. We modify the standard transmission line model (TLM) to include the effects of spatially varying specific contact resistivity ρ_c along the contact length. Both Cartesian and circular (or annular) contacts are analyzed. The local voltage-dependent ρ_c along the contact length is calculated self-consistently by solving the lumped circuit TLM equations coupled with the quantum tunneling model for MIM junctions, or the thermionic emission current injection model for 2D materials. We find that current distribution and contact resistance depend strongly on input voltage, contact dimension and geometry, and material properties. We also propose to reduce contact resistance in 2D-material-based electrical contacts by roughness engineering of the contact interfaces. The results for ohmic contact are verified with finite element method (FEM) based simulations, and the 2D-material based calculations are validated with existing theory and experiments. We further extend this work and demonstrate a method to mitigate current crowding, by engineering the interface layer properties and geometry. We find that current steering and redistribution can be realized by strategically designing the specific contact resistivity ρ_c along the contact length. We also find that introducing a nanometer scale thin insulating tunneling gap between highly conductive contact members can greatly reduce current crowding while maintaining similar total contact resistance.
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