Excimer-Laser Crystallization of Silicon Films: Numerical Simulation of Lateral Solidification
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Mat. Res. Soc. Symp. Proc. Vol. 452 ©1997 Materials Research Society
dT ) K(0, T)dTj dK(0,T)T
CP(0 T T( dt
dx
d )L+
dy
+ S1 (W)+S 2 (tW
(1)
with the initial condition T(0) = preheat temperature, and insulating boundary conditions at the top and the sides, where Cp is the heat capacity, K the thermal conductivity, Si the absorbed laser energy heat source function, the phase-identifier function, and S2 the latent heat function. We utilize the temperature, phase, and vertical- and lateral-position-dependent heat source function in order to model the position-dependent energy deposition process that occurs when a spatially tailored beam, whose energy density may be high enough to initiate melting of the irradiated portion of the film, is incident on the film surface. The model further incorporates the interface response function (IRF) - i.e., systematic variation of the interface velocity as a function of the interfacial undercooling and overheating at the phase boundary. (A linearized IRF with the proportionality constant of 6.7 cm/sK was used.) A similar approach was taken previously in the one-dimensional model that was developed for analyzing pulsed laser melting and solidification of Si surfaces [6,10]. Further details of the model can be found in reference [8]. SIMULATED SAMPLE CONFIGURATION We analyze the thermal response of a thin Si film on SiO 2 (Fig. 1) when it is irradiated with a laterally tailored incident beam so as to induce spatially confined melting and solidification of the film. Such a situation, in which complete melting of the Si film is induced at - and only at - predesignated regions, forms the basis of a new category of ELC processes collectively referred as the artificially-controlled superlateral growth method (ACSLG) [11]. In order to simplify the situation, we have carried out simulations corresponding to melting and solidification of thin crystal Si films, at various energy densities, using a square beam profile whose beam width is fixed at 2 p.m. Specifically, the following values are used in the calculation: a node size of 20 nm was used for the Si film and energy densities of 500 mJ/cm 2 and 800 mJ/cm 2 . As to the specific details of the simulation, we have used the grid of 250 by 5 nodes for representing the Si film, 250 by 55 nodes for representing the substrate. A variable node scheme was used in order to reduce the total computation time without sacrificing the accuracy of the results. The sample configuration that was utilizec4 for the simulation consisted of a 1,000-A-thick Si film on oxide.
Energy
2 lim wide
x
100-A-thick SI film
izizizztz -
TTTT4
5i0 2
Figure 1: A schematic of the sample configuration and the lateral beam profile. The pulse duration of the excimer laser 36ns.
942
RESULTS The simulation results reveal that there are, as shown in Figs. 2 and 3, two distinct types of solidification behavior that are observed depending on the energy density of the incident beam. Figures 2a and 2b show the evolution of the solid-liquid interface during melting an
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