Diploma Thesis Constitutive Law for Single Crystal Silicon (SCSi) based on Molecular Dynamic Potentials

Using the Modified Embedded Atom Method (MEAM) a new material model was made accessible to FEM computations. This new model takes into account the molecular dynamics of diamond cubic crystals. It owns a degree of freedom that is not yet used in other potentials that are utilized: the internal displace-ment of the two sub-lattices in the crystal. This enables the model to reproduce the microscopic relaxation in such crystals as well as the Raman-frequencies in phonon dispersion diagrams that can be measured experimentally. For the case of single crystal silicon (SCSi) all three stiffness moduli were repro-duced. Comparisons with experiments for the determination of the ultimative strength of SCSi showed that it behaves softer than real single crystal silicon. Acknowledgements To Ondrej Papes for all the patience and time he found to support me. To my sister Iren for the time she lost helping me with my poor English. To my co-students Reto Somaini and Andreas Schifferle for all the worthwhile discussions, but also for times of fun. 2y ”Silicon is a test case for the development of empirical potentials for covalent materials. Its great technological importance, the vast amount of relevant ex-perimental and theoretical studies available, and its intrinsic interest as the rep-resentative covalent material make it an ideal candidate for exploring to what extent the empirical potential approach can be exploited.