Size dependence of current-voltage properties in Coulomb blockade networks

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 δ (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 δ. Its exponent γ corresponds to a sensitivity of the threshold depending on δ, and is inversely proportional to N_x (i.e., δ at fixed N _y). Further, the power-law exponent ζ, characterizing the nonlinearity of the I-V property in the intermediate region, logarithmically increases as δ increases. Our simulations describe the experimental result ζ = 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 δ. 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.