Equilibrium shape of thermomigration Al-doped channels in Si wafers

Closed channel structures with interfaces formed by p – n junctions, used in high- current electronics, can be formed by the aluminum thermomigration in single-crystal silicon wafers. The equilibrium shape of self-formed channels, depending on material parameters and structure geometry, corresponds to the minimum of the total elastic energy. The contribution of elastic energy to the shape of formed aluminum-doped thermomigration channels in a single-crystal silicon wafer of (100) orientation is studied and presented in this manuscript. It is found by finite element analysis that the minimum of elastic energy is observed in structures where the channel crystal orientation is rotated by an angle of 45 degrees in the crystallographic plane parallel to the substrate surface. At this angle, the structures have a non-zero tilt to the surface normal, with the slope angle depending on the thickness of the channels and the spacing between them.