A model of wafer bonding by elastic accommodation

Two clean and flat wafers can adhere spontaneously. The technique has recently led to novel electronic and optoelectronic devices. The adhesion arises from short-range interatomic forces between wafer surfaces, which can be represented by a reduction in surface energy associated with the transformation of two surfaces into one interface. The wafers, however, are seldom perfectly flat ; the misfit has to be accommodated by elastic distortion, plastic deformation, or mass transport. We model elastic accommodation in this paper. The distortion causes the wafers to gain elastic energy. If the surface reduction dominates over the elastic energy gain, the wafers will bond. We solve the three dimensional elastic field in the misfit wafers analytically. The conditions for bonding are established, and practical implications discussed.