We use a Boltzmann transport equation (BE) to study time evolution of a photo-excited state in a nanoparticle including phonon-mediated exciton relaxation and the multiple exciton generation (MEG) processes, such as exciton-to-biexciton multiplication and biexciton-to-exciton recombination. BE collision integrals are computed using Kadanoff-Baym-Keldysh many-body perturbation theory based on density functional theory simulations, including exciton effects. We compute internal quantum efficiency (QE), which is the number of excitons generated from an absorbed photon in the course of the relaxation. We apply this approach to chiral single-wall carbon nanotubes (SWCNTs), such as (6,2) and (6,5). We predict efficient MEG in the (6,2) and (6,5) SWCNTs within the solar spectrum range starting at the 2E energy threshold and with QE reaching ∼1.6 at about 3E, where E is the electronic gap.
Singlet fission (SF) process, where a singlet exciton decays into a pair of spin one exciton states which are in the total spin singlet state, is one of the possible channels for multiple exciton generation (MEG). In chiral single-wall carbon nanotubes (SWCNTs) efficient SF is present within the solar spectrum energy range which is shown by the many-body perturbation theory (MBPT) calculations based on the density functional theory (DFT) simulations. We calculate SF excitonto-biexction decay rates R 1→2 and biexciton-to-exction rates R 2→1 in the (6,2), (6,5), (10,5) SWCNTs, and in (6,2) SWCNT functionalized with Cl atoms. Within the solar energy range, we predict R 1→2 ∼ 10 14 −10 15 s −1 , while biexciton-to-exction recombination is weak with R 2→1 /R 1→2 ≤ 10 −2 .SF MEG strength in pristine SWCNTs varies strongly with the excitation energy, which is due to highly non-uniform density of states at low energy. However, our results for (6,2) SWCNT with chlorine atoms adsorbed to the surface suggest that MEG in the chiral SWCNTs can be enhanced by altering the low-energy electronic states via surface functionalization.
We use the Boltzmann transport equation (BE) to study time evolution of a photoexcited state, including phonon-mediated exciton relaxation, multiple exciton generation (MEG), and energy-transfer processes. BE collision integrals are derived using Kadanoff-Baym-Keldysh many-body perturbation theory (MBPT) based on density functional theory (DFT) simulations, including exciton effects. We apply the method to a nanostructured p- n junction composed of a 1 nm hydrogen-terminated Si quantum dot (QD) doped with two phosphorus atoms (SiPH) adjacent to the (6, 2) single-wall carbon nanotube (CNT) with two chlorine atoms per two unit cells adsorbed to the surface. We find that an initial excitation localized on either the QD or CNT evolves into a transient charge-transfer (CT) state where either electron or hole transfer has taken place. The CT state lifetime is about 40 fs. Also, we study MEG in this system by computing internal quantum efficiency (QE), which is the number of excitons generated from an absorbed photon during relaxation. We predict efficient MEG starting at 3 E ≃ 1.5 eV and with QE reaching QE = 1.65 at about 5 E, where E ≃ 0.5 eV is the lowest exciton energy, i.e., the gap. However, we find that including energy transfer and MEG effects suppresses CT state generation.
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