I have found that Ga-doped ZnO can cause tension in lattic both high and low doping concentration as Li+ does. Some literature talks about formation energy. Some discuss the size and preferential occupied site.
One method to tackle this problem is to use molecular or solid state calculations. Once you constructed the wurtzite phase of ZnO you can try to dope this structure sites by Ga. You can compare the energies to obtain the most stable doping site. Comparing with experiment will reveal the accuracy of your model.
Doping ZnO grains with non bivalent ions like Ga^III+ often leads to the formation of inversion domain boundaries on basal (sometimes also pyramidal) planes where these ions segregate to and accumulate in octahedral interstices, covering a specific fraction of these monolayers. The fraction depends on the valence. As octahedral sites are surrounded by 6 O^II-, an average charge of +III is required, e..g a full monolayer of Ga. See a publication by Barf, Walther & Mader in Interface Science.
For doping of ions, we generally use oxides of that ions. Now the dopant ion will occupy that lattice site of host material where the ionic radii mismatch of host and dopant is within the limit of 15%. i.e. the ionic radii should be close.