A transistor includes a bulk semiconductor substrate, and a first source/drain region in the bulk semiconductor substrate separated from a second source/drain region in the bulk semiconductor substrate by a channel region. A first air gap is defined in the bulk semiconductor substrate under the first source/drain region, and a second air gap is defined in the bulk semiconductor substrate under the second source/drain region. A gate is over the channel region. A spacing between the first air gap and the second air gap is greater than or equal to a length of the channel region such that the first and second air gaps are not under the channel region. The air gaps may have a rectangular cross-sectional shape. The air gaps reduce off capacitance of the bulk semiconductor structure to near semiconductor-on-insulator levels without the disadvantages of an air gap under the channel region.