We derive from kinetic arguments discrete-continuum step flow models for epitaxial growth, which are valid in equilibrium as well as far-from-equilibrium growth regimes. Besides the usual adatom densities in such models we in addition account for step adatom densities and kink densities. We analyse various new instabilities, which result from the detailed description of the exchange processes at the steps and demonstrate its dependency on the crystal orientation. Furthermore we will present a numerical algorithm and first results for the derived 2+1 dimensional terrace-step-kink model.
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