Comparative analysis of electron-phonon relaxation in a semiconducting carbon nanotube and a PbSe quantum dot

Abstract

The key features of the phonon-induced relaxation of electronic excitations in the (7,0) zig-zag carbon nanotube (CNT) and the Pb16Se16 quantum dot (QD) are contrasted using a time-domain ab initio density functional theory (DFT) simulation. Upon excitation from the valence to the conduction band (CB), the electrons and holes nonradiatively decay to the band-edge in both materials. The paper compares the electronic structure, optical spectra, important phonon modes, and decay channels in the CNT and QD. The relaxation is faster in the CNT than in the QD. In the PbSe QD, the electronic energy decays by coupling to low-frequency acoustic modes. The decay is nonexponential, in agreement with non-Lorentzian line-shapes observed in optical experiments. In contrast to the QD, the excitation decay in the CNT occurs primarily via high-frequency optical modes. Even though the holes have a higher density of states (DOS), they relax more slowly than the electrons, due to better coupling to low-frequency vibrations. Further, the expected phonon bottleneck is not observed in the QD, as rationalized by a high density of optically dark states. The same argument applies to the CNT. The computed results agree well with experimentally measured ultrafast relaxation time-scales and provide a unique atomistic picture of the electron-phonon relaxation processes.