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## Abstract

This thesis treats optimum experimental design for the parameter estimation problem of mobility parameters in charge transport models of organic semiconductors. The models consist of the van Roosbroeck system, a quasi-electrochemical potential defining equation, and the Extended Gaussian Disorder Model and the Extended Correlated Disorder Model both describing the mobility. The arising problems are very ill-conditioned. The essential points of this work are: • The robust numerical solution of the model equations w.r.t. varying parameters, control parameters, boundary values and initial guesses for iterative methods. • The computation of exact derivatives up to order two, which are necessary for the optimum experimental design problem. This includes derivatives of the model functions and implicitly given derivatives of the solution. The Scharfetter-Gummel scheme is applied to the spatial discretization in one dimension, whereas in two dimensions bilinear finite elements are used. The numerical simulation of the discretized equations is done by a hybrid simulation method consisting of Gummel’s method with a special, problem-adapted stabilization term, a contraction based damping strategy, and a full step Newton method in the end for quadratic convergence near the solution. These strategies are independent of the spatial discretization and are applied to the simulation of a polymer nano-chain attached to the cathode. The simulation of the one dimensional problems are used for the optimum experimental design. The derivatives are computed with automatic differentiation exactly up to machine precision. Therefor we use software tools for the computation of the derivatives of the model functions and solve tangential and adjoint equations of the problem for the parameters and control parameters. With optimum experimental design we plan experiments for newest organic materials, like NRS-PPV and a-NPD. The confidence region of the parameters are reduced by a factor of 100 for NRS-PPV.

Document type: | Dissertation |
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Supervisor: | Bock, Prof. Dr. Dres. h.c. Hans Georg |

Date of thesis defense: | 2 June 2014 |

Date Deposited: | 21 Jul 2014 11:23 |

Date: | 2014 |

Faculties / Institutes: | The Faculty of Mathematics and Computer Science > Dean's Office of The Faculty of Mathematics and Computer Science The Faculty of Mathematics and Computer Science > Department of Mathematics The Faculty of Mathematics and Computer Science > Department of Applied Mathematics |

DDC-classification: | 500 Natural sciences and mathematics 510 Mathematics 530 Physics |

Controlled Keywords: | Simulation, Optimization, Optimum Experimental Design, Organic Semiconductor, Gaussian Disorder Mobility Model |