A convenient formula for the activation energy is obtained from the differential equation for the restoration of damaged lattice during thermal annealing. The dynamics of the restoration of damaged lattice was studied for different implantation conditions and annealing methods. The target temperature during implantation is room temperature (RT), low temperature (liquid nitrogen), or 300 ° C. Annealing temperature region is from 380 ° C to 1067 ° C. It is found that the activation energy is low when a low dose is used for implantation in Si. For example, when a dose of 2 × 10 14 cm 2 is used, the activation energy is only 0.028 eV. But when the As is implanted to a dose of 1 × 10 15 cm 2 , two kinds of activation energy appear. The activation energy at low temperatures is smaller than that at high temperatures. When a dose of 5 × 10 15 cm 2 is used, an amorphous layer appears, therefore there are three kinds of annealing temperature region in the annealing process: the epitaxial regrowth of amorphous layer, the transition region and the high activation energy region. When a dose of 2 × 10 16 cm 2 As is used to implant in Si at low temperature, there are four kinds of annealing temperature region in the annealing process. It is the same as mentioned above but there are two high activation energies in the activation energy region. When As is implanted to a dose of 1 × 10 16 cm 2 at 300 ° C, only three kinds of activation energy region appear. When a high dose is used to implant in Si, after rapid thermal annealing (RTA), the activation energy is greater than that for low dose implantation. The activation energy of B implantation in Si is different from As implantation. Only one activation energy is obtained for low dose B (or P) implantation in Si during RTA. But two activation energies appear for As implantation to a dose of 1 × 10 15 cm 2 in Si during RTA. So, the different activation energy correlates with the different process of damaged lattice restoration. The thermal annealing process of residual defects is observed in TEM.