  By detailed first-principles calculations we show that the Fermi energy and
the Rashba splitting in disordered ternary surface alloys (BiPbSb)/Ag(111) can
be independently tuned by choosing the concentrations of Bi and Pb. The
findings are explained by three fundamental mechanisms, namely the relaxation
of the adatoms, the strength of the atomic spin-orbit coupling, and band
filling. By mapping the Rashba characteristics,i.e.the splitting and the Rashba
energy, and the Fermi energy of the surface states in the complete range of
concentrations. Our results suggest to investigate experimentally effects which
rely on the Rashba spin-orbit coupling in dependence on spin-orbit splitting
and band filling.
