Various structures that include at least one thin layer of an amorphous material on a supporting substrate. One structure generally has a receiving substrate, a central crystalline layer and an amorphous layer, all of which may lack any end of range point defects. Another structure includes an intermediate substrate having an upper face, an upper portion and a lower portion, an amorphous layer that does not contain end of range point defects, and a first crystalline layer containing end of range point defects subjacent the amorphous layer and located in the lower portion; and a supporting substrate bonded to the upper face of the intermediate substrate. That structure can also contain a weakened zone or porous layer to facilitate removal of the first crystalline layer to provide the amorphous layer as an upper layer of the semiconductor structure.