Formation of pn junctions in advanced Si-based transistors employs rapid annealing techniques after ion-implantation in order to increase the electrical activation of dopants while minimizing their diffusion. Over the past decade, these techniques have evolved from rapid thermal processing, with time scales of about 1 s, to millisecond methods accomplished by flashlamps or lasers. Although the dopant behavior in terms of diffusion and electrical activation clearly improves as a result of the shortened time scale, the technology transition has taken place on a largely phenomenological basis with little understanding of the physical mechanism for the improvement. The present work provides the key elements of that understanding based on simulations of the reactions between dopant interstitial atoms and interstitial clusters as well as the host semiconductor lattice. The simulations solve the partial differential equations for diffusion and reaction of interstitial atoms, with activation energies for elementary diffusion and reaction steps computed by Maximum a Posteriori paremeter estimation. The fundamental reason for improvements of diffusion and electrical activation in the millisecond regime is that the short time scale promotes exchange of dopant interstitial atoms with the lattice in preference to exchange with interstitial clusters.