The rare earth 4$f$ hybridization with the GaN valence band

The placement of the Gd, Er, and Yb 4f states within the GaN valence band has been explored by both experiment and theory. The 4$d$ -- 4$f$ photoemission resonances for various rare earth doped GaN thin films (RE $=$ Gd, Er, Yb) provide an accurate depiction of the occupied 4$f$ state placement within the GaN. The resonant photoemission show that the major Er and Gd rare earth 4$f$ weight is at about 5-6 eV below the valence band maximum, similar to the 4$f$ weights in the valence band of many other rare earth doped semiconductors. For Yb, there is very little resonant enhancement of the valence band of Yb doped GaN, consistent with a largely 4$f^{\mathrm{14-\delta }}$ occupancy. The placement of the rare earth 4$f$ levels is in qualitative agreement with theoretical expectations.