  Calcium fluoride has been widely used for light up-/down-conversion
luminescence by accommodating lanthanide ions as sensitizers or activators.
Especially, Yb-doped \ce{CaF2} exhibits unique defect physics, causing various
effects on the luminescence. This makes it vital for high efficiency of devices
to control the defect-clustering, but theoretically principal guidelines for
this are rarely provided. Here we perform the first-principles study on defect
physics in Yb-doped \ce{CaF2} to reveal the thermodynamic transition levels and
formation energies of possible defects. We suggest that the fluorine rich
growth condition can play a key role in enhancing the luminescence efficiency
by facilitating the Yb-clustering and suppressing the defect quenchers in bulk.
Detailed energetics of defect aggregation not only well explains the
experimentally favored Yb-clustering but also presents $n$- or $p$-type doping
method for the cluster control.
