We report k-resolved inverse photoemission results for the unoccupied surface-state bands of the reconstructed Si(100)-(2×1) surface with potassium. The experimental results are compared to the surface-state bands obtained from geometry-optimized total-energy calculations. These self-consistent field calculations suggest an ionic type of bonding of the K atom to the Si substrate up to one-monolayer coverage. The origin of the metallization has to be attributed to the partial occupancy of the Si dangling bonds. The experimental data find the unoccupied surface bands as expected from such a picture, but their energy dispersion is not in full agreement with theory.