The Partial Element Equivalent Circuit (PEEC) method is widely used to model a large variety of electrical systems ranging from interconnects to antennas and packaging. A key aspect in the development of the method is the computation of interaction integrals, namely partial inductances and coefficients of potential. In this work, a novel semi-analytical approach to the computation of the self-interaction integral over rectangular domains is proposed for the zero thickness case as it occurs in the case of the coefficients of potential and partial inductances of very thin conductors and in the surface integral equation based formulation. The proposed semi-analytical formula is verified by comparison with more standard integration schemes.