Simulation of charge transport in multi-island tunneling devices: Application to disordered one-dimensional systems at low and high biases

Although devices have been fabricated displaying interesting single-electron transport characteristics, there has been limited progress in the development of tools that can simulate such devices based on their physical geometry over a range of bias conditions up to a few volts per junction. In this work, we present the development of a multi-island transport simulator, MITS, a simulator of tunneling transport in multi-island devices that takes into account geometrical and material parameters, and can span low and high source-drain biases. First, the capabilities of MITS are demonstrated by modeling experimental devices described in the literature, and showing that the simulated device characteristics agree well with the experimental observations. Then, the results of studies of charge transport through a long one-dimensional (1D) chain of gold nano-islands on an insulating substrate are presented. Current-voltage (IV) characteristics are investigated as a function of the overall chain-length and temperature. Under high bias conditions, where temperature has a minimal effect, the IV characteristics are non-Ohmic, and do not exhibit any Coulomb staircase (CS) structures. The overall resistance of the device also increases non-linearly with increasing chain-length. For small biases, IV characteristics show clear CS structures that are more pronounced for larger chain-lengths. The Coulomb blockade and the threshold voltage (Vth ) required for device switching increase linearly with the increase in chain length. With increasing temperature, the blockade effects are diminished as the abrupt increase in current at Vth is washed out and the apparent blockade decreases. Microscopic investigations demonstrate that the overall IV characteristics are a result of a complex interplay among those factors that affect the tunneling rates that are fixed a priori (island sizes, island separations, temperature, etc.), and the evolving charge state of the system, which changes as the applied source-drain bias (VSD ) is changed. In a system of nano-islands with a broad distribution of sizes and inter-island spacings, the applied bias is divided across the junctions as one would expect of a voltage divider, with larger potential drops across the wider junctions and smaller drops across the narrower junctions. As a result, the tunneling resistances across these wider junctions decrease dramatically, relative to the other junctions, at high VSD thereby increasing their electron tunneling rates. IV behavior at high VSD follows a power-law scaling behavior with the exponent dependent on the length of the chain and the degree of disorder in the system.