Multiple Exciton Generation in Chiral Single-Walled Carbon Nanotubes and Silicon Nanowires: DFT-Based Study Including Competition Between Carrier Multiplication and Phonon-Mediated Relaxation

The conclusion about multiple exciton generation (MEG) efficiency in a nanoparticle can only be made by comprehensive study of different relaxation channels, such as phonon-mediated thermalization, carrier multiplication, etc. Here, we study time evolution of a photo-excited state using Boltzmann transport equation (BE) that includes phonon emission/absorption together with the exciton multiplication and recombination. BE rates are computed using non-equilibrium finite-temperature many-body perturbation theory based on DFT simulations, including exciton effects using RPA-screened Coulomb interaction. We compute rates for both all-singlet MEG and Singlet Fission channels, which are of order 10¹⁴ s^-1. For all-singlet MEG we calculate internal quantum efficiency (QE), the number of excitons generated from a single absorbed photon. Efficient MEG in chiral single-wall carbon nanotubes (SWCNTs), such as (6,2), both pristine and Cl-doped, (6,5), and in nm-sized amorphous H-passivated Si nanowires is present within the solar spectrum range. We predict QE≈1.3-1.6 at the excitation energy of 3 E_gap in (6,2) and (6,5). However, QE=1 is found in CNT (10,5) which suggests strong chirality dependence of MEG. MEG efficiency in functionalized SWCNTs is enhanced compared to the pristine case.