A method for manufacturing a heterostructure, including: contacting a first substrate having a first coefficient of thermal expansion and a second substrate having a different second coefficient of thermal expansion; annealing an assembly formed by contacting the first substrate and the second substrate; after annealing, returning the assembly to room temperature; providing, before the contacting, at least one intermediate layer at a surface of at least one of the first and second substrates, the at least one intermediate layer being made of a material which is ductile during the annealing and returning to room temperature; performing the contacting with the at least one intermediate layer sandwiched between the first and the second substrates; upon returning to room temperature, applying an outer pressure to the assembly to maintain it compressed.