Computer Models of Rapid Solidification
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Computer Models of Rapid Solidification G. H. Gilmer, J. Q. Broughton Bell Laboratories, Murray Hill, New Jersey 07974
ABSTRACT
We discuss some recent simulations of crystal growth from the melt at large values of the undercooling. Molecular dynamics studies of the crystallization of a Lennard-Jones liquid and Monte Carlo simulations of the Ising model have together provided information on several aspects, including maximum growth rates, generation of vacancies and other defects, and impurity trapping. INTRODUCTION New techniques have been developed for the rapid crystallization of metals and semiconductors. Laser annealing, or the thermal processing of crystalline material by means of a laser pulse has been used to achieve large resolidification rates [1]. Crystal-melt interface velocities up to 15 m/s have been reported for silicon [2]. Typically, the substrate is melted to a depth of several microns, and the steep temperature gradients that result also provide rapid cooling after the pulse terminates. Recrystallization starts when the interface cools below the melting point, and the latent heat released is readily transferred to the interior of the crystal. In this case, heat conduction is not the only factor that controls the interface velocity, and the finite rate of atomic rearrangement also causes observable effects. The large amount of data that has become available recently should provide answers to fundamental questions concerning the intrinsic limits to the solidification rate. Rapid solidification also can induce changes in the crystal structure and composition. Material in the region of the interface is, of course, in transition from the fluid to the crystalline state. Generally, as we demonstrate in a later section, the interfacial region is limited in thickness to a few atomic diameters. Therefore, the rearrangement from liquid to crystalline structure must occur in a time of -10-10 sec for velocities of 10 m/s. Some of the properties characteristic of the disordered liquid may be "trapped" in the solid in this case, unless the mobility of the atoms in the interface is extremely large. Laser annealing experiments have demonstrated that certain impurities can be trapped at high concentrations. In some cases, the maximum equilibrium solubility can be exceeded by several orders of magnitude. These new materials may have useful properties. Rapid growth can also lead to a degeneration of the crystal structure. In the case of silicon grown on the (I11) orientation, velocities of -5 m/s produce a number of lattice defects, and at higher velocities the crystalline symmetry is lost completely, and amorphous silicon is formed [2]. Apparently there is not enough time for the atoms to reach the ordered crystal structure. Progress in understanding these phenomena can be made by comparing tfie experimental data with atomic-scale models of solidification. Direct observations of the crystal-melt interface are not possible in most cases, and the experiments yield only information about the rates of solidification a
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