Experimental evidences and microscopic modelling of the mechanism of B diffusion in Si and Ge are given. In both the lattices B migrates by the mediation of self-interstitials (Is). In Si, B diffusion occurs mainly through the formation of a BI0 complex, after interactions of BS-with I0 or with I++ in intrinsic condition or high hole densities, respectively, followed by a proper charge exchange. A small contribution of the BI-complex is visible only under n-type doping, when BS-and I0 bind nonetheless the pairing of B with the n-dopants. Also in Ge, ...