A method for making a semiconductor device may include forming spaced apart gate stacks on a substrate with adjacent gate stacks defining a respective trench therebetween. Each gate stack may include alternating layers of first and second semiconductor materials, with the layers of the second semiconductor material defining nanostructures. The method may further include forming respective source/drain regions within the trenches, respective insulating regions adjacent lateral ends of the layers of the first semiconductor material, and respective conductive contact liners in the trenches.