Dynamics of Charge Transfer and Multiple Exciton Generation in the Doped Silicon Quantum Dot -- Carbon Nanotube System: Density Functional Theory Based Computation

We use Boltzmann transport equation (BE) to study time evolution of a photo-excited 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 nano-structured $p-n$ junction composed of a 1~$nm$ hydrogen-terminated $Si$ quantum dot (QD) doped with two phosphorus atoms ($Si_{36}P_2 H_{42}$) 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 ...