Complex band structure and electronic transmission

TL;DR

This study compares complex band structure and DFT-NEGF transport methods to determine electron decay constants in nano-scale junctions, finding strong agreement in molecular systems and some discrepancies in semi-conductors.

Contribution

It provides a comparative analysis of two primary theoretical approaches for calculating decay constants in nano-scale electronic junctions, highlighting their agreement and differences.

Findings

Strong agreement between methods for molecular junctions

Discrepancies observed in semi-conductor junctions

Template established for channel-resolved length dependence analysis

Abstract

The function of nano-scale devices critically depends on the choice of materials. For electron transport junctions it is natural to characterize the materials by their conductance length dependence, $\beta$. Theoretical estimations of $\beta$ are made employing two primary theories: complex band structure and DFT-NEGF Landauer transport. Both reveal information on $\beta$ of individual states; i.e. complex Bloch waves and transmission eigenchannels, respectively. However, it is unclear how the $\beta$-values of the two approaches compare. Here, we present calculations of decay constants for the two most conductive states as determined by complex band structure and standard DFT-NEGF transport calculations for two molecular and one semi-conductor junctions. Despite the different nature of the two methods, we find strong agreement of the calculated decay constants for the molecular junctions while the semi-conductor junction shows some discrepancies. The results presented here provide a template for studying the intrinsic, channel resolved length dependence of the junction through complex band structure of the central material in the heterogeneous nano-scale junction.