Methods of forming semiconductor structures include transferring a portion (116a) of a donor structure to a processed semiconductor structure (102) that includes at least one non-planar surface. An amorphous film (144) may be formed over at least one non-planar surface of the bonded semiconductor structure, and the amorphous film may be planarized to form one or more planarized surfaces. Semiconductor structures include a bonded semiconductor structure having at least one non-planar surface, and an amorphous film disposed over the at least one non-planar surface. The bonded semiconductor structure may include a processed semiconductor structure and a portion of a single crystal donor structure attached to a non-planar surface of the processed semiconductor structure.