Abstract
Contact resistance and current crowding are important to nanoscale electrical contacts. In this paper, we present a self-consistent model to characterize partially overlapped parallel contacts with varying specific contact resistivity along the contact length. For parallel tunneling contacts formed between contacting members separated by a thin insulating gap, we examine the local voltage-dependent variation of potential barrier height and tunneling current along the contact length, by solving the lumped circuit transmission line model (TLM) equations coupled with the tunneling current self consistently. The current and voltage distribution along the parallel tunneling contacts and their overall contact resistance are analyzed in detail, for various input voltage, electrical contact dimension, and material properties (i.e. work function, sheet resistance of the contact members, and permittivity of the insulating layer). It is found the existing one-dimensional (1D) tunneling junction models become less reliable when the tunneling layer thickness becomes smaller or the applied voltage becomes larger. In these regimes, the proposed self-consistent model may provide a more accurate evaluation of the parallel tunneling contacts. For the special case of constant ohmic specific contact resistivity along the contact length, our theory has been spot-checked with finite element method (FEM) based numerical simulations. This work provides insights on the design, and potential engineering, of nanoscale electrical contacts with controlled current distribution and contact resistance via engineered spatially varying contact layer properties and geometry.
Highlights
For parallel tunneling contacts formed between contacting members separated by a thin insulating gap, we examine the local voltage-dependent variation of potential barrier height and tunneling current along the contact length, by solving the lumped circuit transmission line model (TLM) equations coupled with the tunneling current self consistently
We focus on two situations: and thin tunneling junction with uniform thickness, where analytical solutions to the TLM current and voltage equations are no longer available, and Eqs (5) and (6) are solved numerically
Our model considers the spatial variation of contact resistivity along the contact structure
Summary
Contact resistance and current crowding are important to nanoscale electrical contacts. The current and voltage distribution along the parallel tunneling contacts and their overall contact resistance are analyzed in detail, for various input voltage, electrical contact dimension, and material properties (i.e. work function, sheet resistance of the contact members, and permittivity of the insulating layer) It is found the existing one-dimensional (1D) tunneling junction models become less reliable when the tunneling layer thickness becomes smaller or the applied voltage becomes larger. We provide comprehensive analysis of the effects of contact geometry (i.e. dimension of the contact, and distance between the contact electrodes), and material properties (i.e. work function, sheet resistance of the contact members, and permittivity of the insulating layer) on the spatial distributions of currents and voltages across these contacts, and the overall contact resistance of parallel contacts.
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