The atomic and electronic structures of semiconductor heterostructures, including steps, misfit dislocations and interface disorder, are studied by using the density-functional tight-binding (TB) method. Atomic structures of misfit dislocations both edge type 1/2 <110> (001) and 60° dislocations in the semiconductor heterostructures, like Si-Ge superlattices and GaAs/Si, InAs/GaAs(001), InP/GaAs(001) systems, are studied by using order of N [O(N)] calculational method. The path probability method (PPM) in the statistical physics is used to study the influence of the interface disorder on the electronic properties of the semiconductor heterostructures. It is shown that the junction relaxation influences quite significantly the electronic and mechanical properties of semiconductor heterostructures. The critical layer thickness hc for the generation of misfit dislocations depends significantly on the interface disorder (increase of hc) at the semiconductor heterostructures.

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