The 2D electron gas (2DEG) formed at the surface of SrTiO$_3$(001) has attracted great interest because of its fascinating physical properties and potential as a novel electronic platform, but up to now has eluded a comprehensible way to tune its properties. Using angle-resolved photoemission spectroscopy with and without spin detection we here show that the band filling can be controlled by growing thin SrTiO$_3$ films on Nb doped SrTiO$_3$(001) substrates. This results in a single spin-polarised 2D Fermi surface, which bears potential as platform for Majorana physics. Based on our results it can furthermore be concluded that the 2DEG does not extend more than 2 unit cells into the film and that its properties depend on the amount of SrO$_x$ at the surface and possibly the dielectric response of the system.
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