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The defence will be in English.
Abstract: Organic semiconductor solar cells are one of the emerging technologies for photovoltaics. When a photon arrives at the cell, an exciton, i.e. an electron-hole pair, will be formed on the donor side of the cell (generally a polymer). The exciton will migrate to the interface between the donor and the acceptor (generally a fullerene) and will then dissociate. The electron will pass to the acceptor side while the hole will remain on the donor side, the two will then join the electrodes of the cell.
Understanding what is happening at the interface is crucial since the efficiency of the cell depends heavily on it. One of the key phenomena that takes place there is that the electron which crosses the interface finds itself coupled with the vibrations of the lattice also called phonons. This coupling gives rise to the birth of quasi-particles describing the electron “dressed” by the interaction with the vibration modes of the network, called polarons, the physics of which is complex.
A first part aims to deal with the problem of coupling between the electron and phonons, in a non-perturbative manner. We construct a dynamical mean field theory for the Holstein model which includes an electron coupled to local harmonic phonons. We then present the recursion method which uses an expansion of the Green function in continued fractions and allows a very efficient numerical resolution of the mean field equations.
A second part shows the modeling of the injection of an electron at a donor-acceptor interface for an organic solar cell. We use the approach developed in the first chapter to treat the interaction between the electron and phonons. We introduce a formalism to treat the injection of the electron by looking at its flow. Several variants of the model are analyzed by considering in particular the presence or absence of an electrostatic potential, the nature of the recombination, in a wide or narrow band, or on the donor or acceptor side.
A final part analyzes the transport of the electron once injected on the acceptor side. It is shown that the use of a mean field theory cannot directly describe the propagation of the electron. We also show that the transport of the electron is made up of the succession of two phases, the coherent propagation phase in the network and the coherent propagation phase in the excitation space. We calculate the thermalization length of the electron, at zero and non-zero temperature.
An additional part explores the use of continued fractions and recursion techniques for the dynamical mean field but applied to the Hubbard model. For this purpose, we propose a new Anderson impurity solver based on the equations of motion applied to the retarded Green function. We generate an operator space equipped with a scalar product. Starting from an initial operator, we expand the Green function in a continued fraction. The self-consistency to obtain the dynamical mean field is obtained as in the first part and makes it possible to find the main regimes of the Hubbard model in infinite dimension.
