Erbium (Er) doped GaN (Er:GaN) bulk crystals are promising as an optical gain material for high energy lasers. Other than the preferred configuration of Er3+ occupying the Ga site with four nearest neighbor N atoms (ErGa), Er can also form a complex with a defect (ErGa-DX) in Er:GaN. A set of Er:GaN semi-bulk crystals were grown by hydride vapor phase epitaxy (HVPE) at different growth temperatures to allow the determination of the formation energies, EF, of Er optical centers in Er:GaN. Photoluminescence (PL) emission spectra near 1.5 μm pumped by a near band edge excitation (λexc = 375 nm) and by a resonant excitation (λexc = 980 nm) were measured, which yielded two different formation energies of EF = 2.8 eV and 3.3 eV, corresponding to the formation of ErGa-DX and ErGa in Er:GaN, respectively. As a gain medium, the formation of ErGa-DX in Er:GaN would not only reduce the pumping efficiency of Er optical centers but also increase the optical loss. Our results provide useful insights into possible strategies for enhancing the fraction of ErGa in Er:GaN and, hence, the pumping efficiency, paving the way for achieving optical gain and lasing in Er:GaN.