Synthesis of monolayer FeSe on SrTiO3, with greatly enhanced superconductivity compared to bulk FeSe, remains difficult. Lengthy annealing within a certain temperature window is always required to achieve superconducting samples as reported by different groups around the world, but the mechanism of annealing in inducing superconductivity has not been elucidated. We grow FeSe films on SrTiO3 by molecular beam epitaxy and adjust the stoichiometry by depositing additional small amounts of Fe atoms. The monolayer films become superconducting after the Fe deposition without any annealing, and show similar superconducting transition temperatures as those of the annealed films in transport measurements. We also demonstrate on the 5-unit-cell films that the FeSe multilayer can be reversibly tuned between the non-superconducting $sqrt{5} times sqrt{5}$ phase with Fe-vacancies and superconducting $1 times 1$ phase. Our results reveal that the traditional anneal process in essence removes Fe vacancies and the additional Fe deposition serves as a more efficient way to achieve superconductivity. This work highlights the significance of stoichiometry in the superconductivity of FeSe thin films and provides an easy path for superconducting samples.
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