We have performed an ab initio theoretical investigation of the energetic stability, equilibrium atomic geometry, and scanning tunneling microscope ͑STM͒ images of the Ca/ Si͑111͒ surface. We have considered the ͑3 ϫ 1͒, ͑3 ϫ 2͒, and ͑2 ϫ 1͒ structural models for Ca coverage of 1 / 3 ML, 1 / 6 ML, and 1 / 2 ML, respectively. Our total energy results indicate that the ͑3 ϫ 1͒ phase is not expected to occur, even for Ca-rich conditions. In the ͑3 ϫ 2͒ phase the Ca adatoms lie on the T4 sites along the surface trench separated by Si honeycomb chains. Similarly, in the ͑2 ϫ 1͒ phase the Ca adatoms are adsorbed on the T4 sites of the surface trench separated by Si zigzag chains. The equilibrium geometries and electronic charge transfers between Ca adatoms and Si͑111͒ surface for the ͑3 ϫ 2͒ and ͑2 ϫ 1͒ phases have been detailed. Our simulated STM images indicate that the higher-lying occupied states are located on the topmost Si atoms along the chains, while the empty states lie on the Ca adatoms, forming bright spots and stripes on the ͑3 ϫ 2͒ and ͑2 ϫ 1͒ surfaces. For occupied states, the simulated STM images confirm the experimentally verified 2ϫ modulation along the honeycomb chains in the Ca/ Si͑111͒-͑3 ϫ 2͒ surface, induced by attractive interactions between Ca adatoms and the nearest-neighbor Si atoms. Finally we have calculated the electronic band structures for the energetically stable ͑3 ϫ 2͒ and ͑2 ϫ 1͒ phases of the Ca/ Si͑111͒ surface, and compared ͑in detail͒ with the recent experimental findings.