One illustrative method disclosed herein includes forming a plurality of spaced-apart fin structures in a semiconductor substrate, wherein the fin structures define a portion of an alignment/overlay mark trench where at least a portion of an alignment/overlay mark will be formed, forming at least one layer of insulating material that overfills the alignment/overlay mark trench and removing excess portions of the layer of insulating material positioned above an upper surface of the plurality of fins to thereby define at least a portion of the alignment/overlay mark positioned within the alignment/overlay mark trench. A device disclosed herein includes a plurality of spaced-apart fin structures formed in a semiconductor substrate so as to partially define an alignment/overlay mark trench, an alignment/overlay mark consisting only of at least one insulating material positioned within the alignment/overlay mark trench, and a plurality of FinFET semiconductor devices formed in and above the substrate.