A method for manufacturing a semiconductor structure that comprises providing a monocrystalline silicon base layer comprising a first region for manufacturing the III-N semiconductor device and a second region for manufacturing the silicon semiconductor device; providing on the monocrystalline silicon base layer a mask layer, the mask layer being interrupted, in the first region, by a recess in the monocrystalline silicon base layer, wherein the mask layer comprises a 2D material; forming, selectively, a layer of gamma-Al2O3 at the bottom of the recess by a first growth process; forming, selectively on the layer of gamma-Al2O3, a III-N semiconductor device stack by a second growth process, and thereafter; manufacturing, in the second region, at least partially a silicon semiconductor device.