Monte Carlo Simulation of the Rapid Crystallization of Bismuth-Doped Silicon

Kenneth A. Jackson, I George H. Gilmer, 2 and Dmitri E. Temkin 3tMaterials Science and Engineering, Universi_.' of Arizona. Tucson. Arizona 857122AT&T Bell Laboratories, Murray Hill, New Jersey 079743Central Scientific-Research Institute of Ferrous Metallurgy. Moscow 107005. Russia(Received 17 January 1995)/_t+<,4 ,, ,', J U 'In this Letter we report Ising model simulations of the growth of alloys which predict quite differentbehavior near and far from equilibrium. Our simulations reproduce the phenomenon which has beentermed "solute trappirlg," where concentrations of solute, which are far in excess of the equilibriumconcentrations, are observed in the crystal after rapid crystallization. This phenomenon plays animportant role in many processes which involve first order phase changes which take place underconditions far from equilibrium. The underlying physical basis for it has not been understood, but theseMonte Carlo simulations provide a powerful means for investigating it.