Ge is becoming an increasingly popular semiconductor material with high Si compatibility for on-chip optical interconnect technology. For a better manifestation of the meritorious material properties of Ge, its surface treatment should be performed satisfactorily before the electronic and photonic components are fabricated. Ex-situ rapid thermal annealing (RTA) processes with different gases were carried out to examine the effects of the annealing gases on the thin-film quality of Ge grown epitaxially on Si substrates. The Ge-on-Si samples were prepared in different structures using the same equipment, reduced-pressure chemical vapor deposition (RPCVD), and the samples annealed in $N_2$, forming gas (FG), and $O_2$ were compared with the unannealed (deposited and only cleaned) samples to confirm the improvements in Ge quality. To evaluate the thin-film quality, room-temperature photoluminescence (PL) measurements were performed. Among the compared samples, the $O_2$-annealed samples showed the strongest PL signals, regardless of the sample structures, which shows that ex-situ RTA in the $O_2$ environment would be an effective technique for the surface treatment of Ge in fabricating Ge devices for optical computing systems.