First-principles study of the variation of electron transport in a single molecular junction with the length of the molecular wire

Abstract

We report a first-principles study of quantum transport in a prototype two-terminal device consisting of a molecular nanowire acting as an inter-connect between two gold electrodes. The wire is composed of a series of bicyclo[1.1.1]pentane (BCP) cage-units. The length of the wire $(L)$ is increased by sequentially increasing the number of BCP cage units in the wire from 1 to 3. A two terminal model device is made out of each of the three wires. A parameter free, nonequilibrium Green's function approach, in which the bias effect is explicitly included within a many body framework, is used to calculate the current-voltage characteristics of each of the devices. In the low bias regime that is considered in our study, the molecular devices are found to exhibit Ohmic behavior with resistances of 0.12, 1.4, and $6.5\text{ }\ensuremath{\mu}\ensuremath{\Omega}$ for the wires containing one, two, and three cages respectively. Thus the conductance value, ${G}_{c}$, which is the reciprocal of resistance, decreases as ${e}^{\ensuremath{-}\ensuremath{\beta}L}$ with a decay constant $(\ensuremath{\beta})$ of $0.59\text{ }{\text{\AA{}}}^{\ensuremath{-}1}$. This observed variation of conductance with the length of the wire is in excellent agreement with the earlier reported exponential decay feature of the electron transfer rate predicted from the electron transfer coupling matrix values obtained using the two-state Marcus-Hush model and the Koopman's theorem approximation. The downright suppression of the computed electrical current for a bias up to 0.4 V in the longest wire can be exploited in designing a three terminal molecular transistor; this molecular wire could potentially be used as a throttle to avoid leakage gate current.