A Theoretical Study of Charge

The main objective of this thesis is to provide a deeper understanding of the charge transport phenomena occuring in molecular crystals. The focus is on the stability and the dynamics of the polaron as the charge carrier. To achieve this goal, a series of numerical calculations are performed using the semi-emprical "Holstien-Peierls" model. The model considers both intra(Holstein) and inter(Peierls) molecular interactions, in particular the electron-phonon interactions. First, the stability of the polaron in an ordered two dimensional molecular lattice with an excess charge is studied using Resilient backPropagation, RPROP, algorithm. The stability is defined by the "polaron formation energy". This formation energy is obtained for a wide range of parameter sets including both intraand inter-molecular electron-phonon coupling strengths and their vibrational frequencies, transfer intergral and electric field. We found that the polaron formation energies lying in the range of 50-100 meV are more interesting for our studies. The second step to cover is the dynamical behaviour of the polaron. Using the stable polaron solutions acheived in the first step, an electric field is applied as an external force, pushing the charge to move. We observed that the polaron remains stable and moves with a constant velocity for only a limited range of parameter sets. Finally, the impact of disorder and temperature on the charge dynamics is considered. Adding disorder to the system will result in a more restricted parameter set space for which the polaron is dynamically stable and mobile. Temperature is included in the Newtonian equations of motion via a random force. We observed that the polaron remains localized and moves with a diffusive behaviour up to a certain temperature. If the temperature increases to values above this critical temperature, the localized polaron becomes delocalized. All this research work is coded in MATLAB software , allowing us to run the calculations, test and validate our results.