We report the development of a method for calculating the electronic structure of semiconductor surfaces. It is based on the Koster-Slater idea for treating localized perturbations, which was later extended to describe surfaces. The present method makes use of semiempirical tight-binding Hamiltonians and of a novel way to create free surfaces. A Green's-function scattering-theoretical formulation is employed. The properties of the bulk crystal are built in and preserved. Bound-surface-state energies are determined unambiguously and accurately even for states whose wave functions are very extended. The total and local changes occurring in the density of states due to the surface can be calcualted directly, and therefore very accurately, without having to subtract two large quantities. Some of the structure in the state-density changes is in the form of narrow peaks, which can be identified as resonances or antiresonances. In order to point out advantages of the method and to compare our results with the results of slab calculations, we present applications to the Si and Ge (100) free surfaces. The present method is shown to be very efficient, accurate, and fast. Despite the fact that a tight-binding Hamiltonian of a truly semi-infinite system is treated exactly, the method employs matrices which are much smaller than those arising in slab calculations. Finally, the method is applied to a study of the (100) surfaces of the isoelectronic series Ge-GaAs-ZnSe and to the (100) surfaces of cubic SiO2. © 1978 The American Physical Society.