Atomic layer etching (ALE) of GaN on silicon substrates has been investigated using fluorine-based chemistry. The ALE process used for this study consists of a modification step using SF6 plasma and a removal step using argon plasma. Two configurations were studied in which the distance between the sample and the plasma source was modified. The energy scan, synergy, selective etching of GaFx by Ar+ ion bombardment, and self-limiting etching regime of the ALE of GaN were first investigated. An etch per cycle of 0.50 nm/cycle averaged over 100 cycles was reached for GaN ALE. The self-limiting regime was also obtained for both SF6 and argon plasma steps. Moreover, a synergy rate as high as 78% was achieved. It was found that the GaFx-modified layer can be selectively sputtered by applying a self-bias voltage while the argon ion energy is maintained below the sputtering threshold of GaN.