Electronic Structure and Scaling of Coulomb Defects in Carbon Nanotubes from Modified Hückel Calculations

• Published in: Journal of physical chemistry. C 2023-12, Vol.127 (49), p.23760-23767
• Main Authors: Eckstein, Klaus H., Hertel, Tobias
• Format: Article
• Language: English
• Subjects: C: Spectroscopy and Dynamics of Nano, Hybrid, and Low-Dimensional Materials
• ISSN: 1932-7447; 1932-7455
• DOI: 10.1021/acs.jpcc.3c06007

Controlled doping and understanding its underlying microscopic mechanisms are crucial for the advancement of nanoscale electronic technologies, especially in semiconducting single-wall carbon nanotubes (s-SWNTs), where adsorbed counterions are known to govern redox-doping levels. However, modeling the associated “Coulomb defects” at low doping levels is challenging due to the need for large-scale simulations. Here, modified Hückel calculations on 120 nm long s-SWNTs with adsorbed Cl– ions are used to study the scaling properties of shallow Coulomb defect states at the valence band edge and quantum well (QW) states in the conduction band. Interestingly, the QW states may underlie the observed exciton band shifts of inhomogeneously doped semiconductors. Using a variational approach, the binding energies of Coulomb defects are found to scale with counterion distance, effective band mass, relative permittivity, and counterion charge as d α − 2 m α − 1 ϵ r − α | z j | α , where α is an empirical parameter, deepening our understanding of s-SWNT doping.