Variability and self-average of impurity-limited resistance in quasi-one dimensional nanowires

The impurity-limited resistance in quasi-one dimensional (quasi-1D) nanowires is studied under the framework of the Lippmann-Schwinger scattering theory. The resistance of cylindrical nanowires is calculated theoretically under various spatial configurations of localized impurities with a simplified short-range scattering potential. Then, the relationship between the phase interference and the variability in the impurity-limited resistances is clarified. We show that there are two different and independent mechanisms leading to the variability in impurity-limited resistances; incoherent and phase-coherent randomization processes. The latter is closely related to the so-called “self-average” and its physical origin under nanowire structures is clarified. We point out that the ensemble average also comes into play in the cases of long channel nanowires, which leads to the self-average resistance of multiple impurities.