According to thermodynamic and kinetic theory,considering the variation of bulk free energy and superficial energy after nucleation as well as the migration of atoms,we study systematically the planar nucleation and crystallization that relate to two possible transition mechanisms in the annealing process of ion implanted S i：（1） liquid/solid transition：the critical nucleation work is equal to half the increased superficial energy and inversely proportional to the supercoolingΔT.Compared with bulk nucleation,the radius of the critical nucleus decreases by half,and the nucleation rate attains its maximum at T = Tm/2.（2） amorphous/crystalline transition：the atoms contained in the critical nucleus and situated on its surface,as well as critical nucleation work,are all directly proportional to the height of the nucleus,and the nucleation barrier is equal to half the superficial energy too.In addition,we take SiGe semiconductor as a specific example for calculation;a value of 0.03 eV/atom is obtained for the elastic strain energy,and a more reasonable result can be gotten after taking into account its effect on transition Finally,we reach the following conclusion as a result of the calculation：for the annealing of ion implanted Si,no matter what the transition method is—liquid or solid planar nucleation—the recrystallization process is actually carried out layer by layer on the crystal substrate,and the probability of forming a＂rod-like＂nucleus is much larger than that of a＂plate-like＂nucleus.
