  We report thermoelectric power experiments in e-doped thin films of SrTiO$_3$
(STO) which demonstrate that the electronic band degeneracy can be lifted
through defect management during growth. We show that even small amounts of
cationic vacancies, combined with epitaxial stress, produce a homogeneous
tetragonal distortion of the films, resulting in a Kondo-like resistance upturn
at low temperature, large anisotropic magnetoresistance, and non-linear Hall
effect. Ab-initio calculations confirm a different occupation of each band
depending on the degree of tetragonal distortion. The phenomenology reported in
this paper for tetragonally distorted e-doped STO thin films, is similarto that
observed in LaAlO$_3$/STO interfaces and magnetic STO quantum wells.
