A semiconductor device and fabrication method are described for integrating stacked top and bottom nanosheet transistors by providing a nanosheet transistor stack having bottom and top Si/SiGe superlattice structures (11-14, 17-20) which are separated from one another by a barrier oxide layer (15) and which are separately processed to form first remnant silicon germanium nanosheet layers (12, 14) in the bottom Si/SiGe superlattice structures having a first gate length dimension (DG1) and to form second remnant silicon germanium nanosheet layers (18, 20) in the top Si/SiGe superlattice structures having a second, smaller gate length dimension (DG2) so that the nanosheet transistor stack may then be processed to simultaneously form bottom and top gate electrodes which replace, respectively, the first and second remnant silicon germanium nanosheet layers.