Non-Equilibrium Two-Dimensional Model of Excimer-Laser Melting and Solidification of Thin Si Films on SiO 2
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Vikas V. Gupta, H. Jin Song, and James S. Im Department of Chemical Engineering, Materials Science, and Mining Engineering, Columbia University, New York, NY 10027 ABSTRACT We have developed a two-dimensional numerical model of excimer-laser melting and solidification that properly takes into account the non-equilibrium and transient nature of the process. The model incorporates a novel explicit finite difference scheme for efficiently solving the heat conduction equation and an algorithm that incorporates the interface response function for properly simulating the evolution of phase domains. The model provides space- and timeresolved information regarding the thermal profile and phase domains from which nearly all of the important solidification details can be extracted (e.g., interface location, solidification velocity, interfacial undercooling, etc.). For the simple partial-melting-and-vertical-regrowth scenario, results from the model converge with the results from the well-established onedimensional model. As a result of its two-dimensional and non-equilibrium formulation, which also respects the amorphous and inert nature of the underlying oxide surface, the model is unique in its capability for properly simulating those solidification scenarios that involve extensive lateral growth of solids, as for example those behind the super-lateral growth phenomenon and various artificially controlled super-lateral growth processes. INTRODUCTION Excimer-laser crystallization (ELC) of thin Si films on SiO 2 is a highly transient process that involves rapid melting and solidification of the films. Previous experimental and theoretical studies on the relevant phase-transformation scenarios have definitively revealed that far-fromequilibrium conditions can readily prevail and that a two-dimensional character-in terms of heat flow and transformations-is integral to the process [1,2]. In part, such scenarios are introduced as a consequence of the fact that the films are very thin and that the films rest on top of an SiO 2 surface; the chemical stability and amorphous nature of SiO 2 make the surface a nonparticipating entity as far as the interface-led transformation is concerned (i.e., it neither initiates regrowth nor effectively nucleates crystals). As noted previously, a rigorous and quantitative treatment of the situation is well beyond the scope of any analytical approach because the situation contains a number of nonlinear elements andis highly transient [2]. On the other hand, the problem should be tractable via properly formulated numerical codes. The one-dimensional ELC numerical model that was utilized by a number of investigators [3,4,5] has been identified as being insufficient and, for certain situations, thoroughly misleading [2]. Likewise, available two-dimensional models [6,7]-as discussed in more detail below-are not fully appropriate for simulating the solidification scenarios that are observed in ELC of thin Si films. In this paper, we present a newly developed model, based on the finite difference met
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