Shallow $p^+-n$ junctions were formed by ion implantation and dual-step annealing processes. The dopant implantation was performed into the crystalline substrates using BF$_2$ ions. The annealing was performed with a rapid thermal processor and a furnace. FA+RTA annealing sequence exhibited better junction characteristics than RTA+FA thermal cycle from the viewpoint of junction depth and sheet resistance. A new simulator is designed to model boron diffusion in silicon. The model which is used in this simulator takes into account nonequilibrium diffusion, reactions of point defects, and defect-dopant pairs considering their charge states, and the dopant inactivation by introducing a boron clustering reaction. Using initial conditions and boundary conditions, coupled diffusion equations are solved successfully. The simulator reproduced experimental data successfully.