Provided are contact photomasks and methods using such photomasks for fabricating semiconductor devices and forming contact plugs on portions of active regions exposed between gate lines. The elongated active regions are arrayed in a series of parallel groups with each group being, in turn, aligned along their longitudinal axes to form an acute angle with the gate lines. The contact photomask includes a plurality of openings arranged in parallel lines that are aligned at an angle offset from previously formed gate lines and which may be parallel to the active regions or may be aligned at an angle offset from the axes of both the groups of active regions and the gate lines. Processes for forming contact plugs using such photomasks may provide increased processing margin and extend the utility of conventional exposure equipment for semiconductor devices exhibiting increased integration density and/or built to more demanding design rules.