  Complex doping schemes in RE$_3$Al$_5$O$_{12}$ (RE=rare earth element) garnet
compounds have recently led to pronounced improvements in scintillator
performance. Specifically, by admixing lutetium and yttrium aluminate garnets
with gallium and gadolinium, the band-gap was altered in a manner that
facilitated the removal of deleterious electron trapping associated with cation
antisite defects. Here, we expand upon this initial work to systematically
investigate the effect of substitutional admixing on the energy levels of band
edges. Density functional theory was used to survey potential admixing
candidates that modify either the conduction band minimum (CBM) or valence band
maximum (VBM). We considered two sets of compositions based on
Lu$_3$B$_5$O$_{12}$ where B = Al, Ga, In, As, and Sb; and RE$_3$Al$_5$O$_{12}$,
where RE = Lu, Gd, Dy, and Er. We found that admixing with various RE cations
does not appreciably effect the band gap or band edges. In contrast,
substituting Al with cations of dissimilar ionic radii has a profound impact on
the band structure. We further show that certain dopants can be used to
selectively modify only the CBM or the VBM. Specifically, Ga and In decrease
the band gap by lowering the CBM, while As and Sb decrease the band gap by
raising the VBM. These results demonstrate a powerful approach to quickly
screen the impact of dopants on the electronic structure of scintillator
compounds, identifying those dopants which alter the band edges in very
specific ways to eliminate both electron and hole traps responsible for
performance limitations. This approach should be broadly applicable for the
optimization of electronic and optical performance for a wide range of
compounds by tuning the VBM and CBM.
