where V b is the bias voltage applied to the electrode. µ L and µ R are the two electrochemical potentials on either side of electrodes. T (E, V b ) is the transmission coefficient at energy E and applied bias voltage V b . Similarly, f(E) is the Fermi-Dirac distribution function.The electron transmission function and the current flow through the AuNW at finite bias have been calculated using the post-processing tool TBTrans which is included in the TranSIESTA module.