We present the detailed results of self-consistent and geometry-optimized total-energy, band-structure, and charge-density calculations for a potassium-covered Si(001)-(2×1) surface, and for an unsupported potassium monolayer. We found that the (2×1) reconstruction and the dimer bonds of the Si surface continue to be stable after the adsorption of alkali-metal atoms. At the monolayer coverage the charge from the adsorbed potassium atoms is transferred into the empty, antibonding dangling-bond surface states, resulting in the metallization of the Si(001) substrate surface. The bonding between the overlayer and the substrate surface is ionic, and the Fermi level is pinned by the partially filled silicon surface states. Our theory for the metallization and the surface collective excitations is different from previous ones developed for an alkali-metal overlayer on a metal substrate which suggest that the system undergoes a Mott transition, and can successfully account for recent experimental observations. The presence of the active dangling-bond states prevents the alkali-metal monolayer from metallization, and thus provides the crucial difference between metal and semiconductor substrates. © 1988 The American Physical Society.