[en] Using ab initio calculations, atomic structure and electronic properties of Si(1 1 1)$\sqrt{3}\times <!--\; ??\; -->\sqrt{3}$-Bi surface modified by adsorption of 1/3 monolayer of alkali metals, Li, Na, K, Rb and Cs, have been explored. Upon adsorption of all metals, a similar atomic structure develops at the surface where twisted chained Bi trimers are arranged into a honeycomb network and alkali metal atoms occupy the $T_4$ sites in the center of each honeycomb unit. Among other structural characteristics, the greatest variation concerns the relative heights at which alkali metals reside with respect to Bi-trimer layer. Except for Li, the other metals reside higher than Bi layer and their heights increase with atomic number. All adsorbed surface structures display similar electron band structures of which the most essential feature is metallic surface-state band with a giant spin splitting. This electronic property allows one to consider the Si(1 1 1)$\sqrt{3}\times <!--\; ??\; -->\sqrt{3}$-Bi surfaces modified by alkali metal adsorption as a set of material systems showing promise for spintronic applications. (paper)