We demonstrate how a saddle point search method can be used to study dislocation mobility in a covalent material-a non-trivial transition mechanism in a complex system. Repeated saddle point searches have been carried out by using the minimum mode following algorithm and dimer method in combination with several empirical potential functions for silicon in order to determine the mechanisms for the creation and migration of kinks on a non-dissociated screw dislocation in a silicon crystal. For the environment-dependent interatomic potential, three possible kink migration processes have been identified with activation energies of 0.17, 0.25, and 0.33 eV. The Lenosky potential gives a single, low energy migration mechanism with an activation energy of 0.07 eV, in good agreement with density functional theory results. The kink formation mechanism determined using this potential has an activation barrier of 1.2 eV. Calculations were also carried out with the Tersoff potential, Stillinger-Weber potential and Bolding-Andersen potential. The various potential functions give quite different results for the kink structure and the mechanism of transition.