Coverage dependence of the electronic structure of potassium adatoms on the Si(001)-(2×1) surface

The electronic structure of potassium adatoms on the Si(001)-(2×{}1) surface is studied by first-principles calculations within the local-density-functional theory for a wide range of the K coverage ({Θ}) including low {Θ} values with negligibly small direct interactions among adatoms. The symmetric dimer model is assumed for the substrate Si which is modeled by a ten-layer slab. As possible adsorption sites for K, a raised site on the Si dimer chain and/or a valley site between two dimer chains are considered. The calculations are performed for {Θ} ranging from (1/6 to 1 in units of Si monolayers including the Levine model ({Θ}=(1/2) and also recently proposed double-layer model ({Θ}=1). No free-electron-like surface band characteristic of the K 4s state appears in the Si gap even for higher {Θ}. However, the two gap states originating from the Si dangling bonds in the limit of {Θ}{→}0 shift to higher binding energies by {~}0.5 eV with increasing {Θ} due to the kinetic energy lowering caused by the delocalization of their wave functions toward the overlayer. This is interpreted as a result of the Si-K hybridization which leads to the polarized covalent Si-K bond. The adatom region is essentially neutral even for lower {Θ} if the charge density is averaged in a K sphere, which implies that the adatom-induced dipole moment to reduce the work function shold be attributed to the adatom polarization due to the Si-K orbital mixing rather than the conventional {Θ}-dependent charge transfer.