Quantum correlated electron dynamics in a quantum-dot sensitized solar cell: Keldysh function approach

Abstract

In this work we study quantum dynamics of an electron transferred from a quantum dot (QD) to a semiconductor (SM) in a quantum-dot-semiconductor solar cell. The proposed theoretical description includes the following interactions: electron-electron and electron-phonon interactions in a QD, interaction with light, electron-phonon interaction in an SM, and interaction between the electronic states in a QD and an SM in the tunneling approximation. The interaction of a QD electron with light is considered in the dipole approximation. e-e interaction in a QD is important because electron transition takes place from a QD excitonic state; $e$-ph interaction is necessary to describe relaxation from a QD excitonic state to the valence band and also for the correct description of electron transfer to a semiconductor. $e$-ph interaction in an SM along with the tunneling term describe forward and backward electron transfers from a semiconductor to a quantum dot as well as electron relaxation from an SM conduction band to a valence one. The main goal of this work is to present a theoretical scheme for the calculation of photocurrent in a solar cell where all the interactions mentioned above are present. The expression for photocurrent is presented in terms of SM and QD Keldysh functions that can be found from the proper Dyson equations. If the SM $e$-ph interaction is not considered, the derived Dyson equations are exact. If the SM $e$-ph interaction is included, the Dyson equations for nonequilibrium Green's functions can also be derived only for wide-gap semiconductors where Migdal's theorem is valid, i.e., assuming that ${\ensuremath{\omega}}_{D}/{\ensuremath{\varepsilon}}_{F}\ensuremath{\ll}1$ (${\ensuremath{\omega}}_{D}$ is the Debye frequency and ${\ensuremath{\varepsilon}}_{F}$ is the Fermi energy in the semiconductor). Within the proposed computational scheme we are able to explain the effects of electron-electron and electron-phonon correlations and therefore describe multiexciton generation and hot carrier transitions as well.