Size Dependence of Current-Voltage Properties in Coulomb Blockade Networks

TL;DR

This paper uses Monte Carlo simulations to analyze how the current-voltage characteristics of two-dimensional Coulomb blockade arrays depend on their aspect ratio, revealing power-law behaviors and aligning with experimental findings.

Contribution

It introduces a theoretical model describing size-dependent I-V properties in Coulomb blockade networks, extending one-dimensional results to two dimensions and matching experimental data.

Findings

The CB threshold follows a power-law decay with aspect ratio.

The nonlinearity exponent increases logarithmically with aspect ratio.

The asymptotic I-V behavior converges to Ohm's law at high voltages.

Abstract

We theoretically investigate the current-voltage (I-V) property of two-dimensional Coulomb blockade (CB) arrays by conducting Monte Carlo simulations. The I-V property can be divided into three regions and we report the dependence of the aspect ratio delta (namely, the lateral size N_{y} over the longitudinal one N_{x}). We show that the average CB threshold obeys a power-law decay as a function of delta. Its exponent gamma corresponds to a sensitivity of the threshold depending on delta, and is inversely proportional to N_{x} (i.e., delta at fixed N_{y}). Further, the power-law exponent zeta, characterizing the nonlinearity of the I-V property in the intermediate region, logarithmically increases as delta increases. Our simulations describe the experimental result zeta=2.25 obtained by Parthasarathy et al. [Phys. Rev. Lett. 87 (2001) 186807]. In addition, the asymptotic I-V property of one-dimensional arrays obtained by Bascones et al. [Phys. Rev. B. 77 (2008) 245422] is applied to two-dimensional arrays. The asymptotic equation converges to the Ohm's law at the large voltage limit, and the combined tunneling-resistance is inversely proportional to delta. The extended asymptotic equation with the first-order perturbation well describes the experimental result obtained by Kurdak et al. [Phys. Rev. B 57 (1998) R6842]. Based on our asymptotic equation, we can estimate physical values that it is hard to obtain experimentally.