# A Two Dimensional Tunneling Resistance Transmission Line Model for Nanoscale Parallel Electrical Contacts

## TL;DR

This paper introduces a self-consistent two-dimensional tunneling resistance transmission line model for nanoscale parallel electrical contacts, improving accuracy over 1D models especially at small tunneling layers or high voltages.

## Contribution

It presents a novel 2D model that accurately characterizes current distribution and contact resistance in nanoscale tunneling contacts, surpassing traditional 1D models in certain regimes.

## Key findings

- The model accurately predicts voltage-dependent potential barrier variation.
- It shows 1D models are less reliable at small tunneling layers or high voltages.
- Provides design insights for nanoscale electrical contacts.

## 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. 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.

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Source: https://tomesphere.com/paper/1906.09188