  We present a detailed analysis of the band structure of the
BiAg$_2$/Ag/Si(111) trilayer system by means of high resolution Angle Resolved
Photoemission Spectroscopy (ARPES). BiAg2/Ag/Si(111) exhibits a complex spin
polarized electronic structure due to giant spin-orbit interactions. We show
that a complete set of constant energy ARPES maps, supplemented by a modified
nearly free electron calculation, provides a unique insight into the structure
of the spin polarized bands and spin gaps. We also show that the complex gap
structure can be continuously tuned in energy by a controlled deposition of an
alkali metal.
