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Controlled doping and understanding its underlying microscopic mechanisms iscrucial for advancement of nanoscale electronic technologies, especially insemiconducting single-wall carbon nanotubes (s-SWNTs), where adsorbedcounterions are known to govern redox-doping levels. However, modeling theassociated 'Coulomb defects' is challenging due to the need for large-scalesimulations at low doping levels. Using modified H\"uckel calculations on 120nm long s-SWNTs with adsorbed $\rm Cl^-$ ions, we study the scaling propertiesof shallow Coulomb defect states at the valence band edge and quantum well (QW)states in the conduction band. Interestingly, the QW states may underlieobserved exciton band shifts of inhomogeneously doped semiconductors. Bindingenergies of Coulomb defects are found to scale with counterion distance,effective band mass, relative permittivity and counterion charge according to$d^{\alpha-2}m^{\alpha-1}\epsilon_r^{-\alpha}|z_j|^{\alpha}$, with $\alpha$ asan empirical parameter, deepening our understanding of s-SWNT doping.

Electronic Structure and Scaling of Coulomb Defects in Carbon Nanotubes from Modified H\"uckel Calculations