A method according to some embodiments of the invention includes defining an active region by forming a trench device isolation region on an integrated substrate, forming a mask pattern that exposes a channel sub-region of the active region and the trench device isolation region adjacent to the channel sub-region, etching the trench device isolation region, which is exposed by the mask pattern, to be recessed to a first depth using the mask pattern as an etch mask, etching the channel sub-region to form a gate trench having a second depth that is deeper than the first depth using the mask pattern as an etch mask, and forming a recess gate that fills the gate trench.