Modeling the formation of spontaneous wafer direct bonding under low temperature

Low temperature wafer direct bonding is one of critical technologies in micro/nano fabrication. In this study, a description of interfacial requirements for spontaneous wafer direct bonding under low temperature is proposed. The model relates the occurrence of bonding to interfacial adhesion energy, interfacial nano-topography and elasticity of wafers. Its derivation is based on Johnson-Kendall-Roberts (JKR) theory and a competition between the bonding energy and the deformation of interfacial micro/nano-roughness. The analysis identifies three bonding possibilities, namely spontaneous bonding without voids, spontaneous bonding with voids, and bonding under external pressure with gap or un-bondable. To verify the model, experiments were carried out for silicon wafers with different surface nano-scale roughness.