Pattern formation during stationary heating and zone melting recrystallization of a silicon thin film

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INTRODUCTION

THE zone melting recrystallization (ZMR) process is a kind of directional solidification process which has been used to make single-crystalline Si films from polycrystalline films.[1–4] A silicon film on an insulator material can be produced economically by a graphite-strip, heater-based ZMR process. For full application of the material, the Si film on the insulator should be a low-defect-density singlecrystal film.[5] However, due to the radiational undercooling resulting from the difference of reflectivity between solid and liquid Si, the planar solid/liquid (S/L) interface is unstable and grows with a cellular or dendritic structure, depending on processing variables such as input power density, substrate moving velocity, and radiation width.[1] A qualitative model that describes and predicts the shape of the solidification interface was developed by Im.[1] The model supports the theory that the change in the reflectivity of the Si film upon melting is an important factor in determining the S/L interface in the ZMR process. In situ observation of the S/L interface formed during stationary heating of Si film revealed many interesting microstructural features, including the formation of Si particles in the liquid Si phase, liquid droplets embedded in solid Si, and various S/L interface patterns, ranging from a cellular structure, to a cellular-dendritic structure, to an irregular structure, depending on the process variables. However, simulation of pattern formation during ZMR of Si film has not been performed yet, to our knowledge, even though the linear[6,7] or weakly nonlinear stability analysis[8,9] has been done successfully. In this study, a phase-field model was employed to simulate pattern formation during stationary heating and ZMR WON TAE KIM, Associate Professor, is with RASOM and the Department of Physics, Chongju University, Chongju, 360-704, Korea. SEONG GYOON KIM, Associate Professor, is with RASOM and the Department of Materials Science and Engineering, Kunsan National University, Kunsan, 573-360 Korea. JAE SANG LEE, Postdoctoral Fellow, and TOSHIO SUZUKI, Professor, are with the Department of Metallurgy, The University of Tokyo, Tokyo 113, Japan. Manuscript submitted April 29, 1998.

METALLURGICAL AND MATERIALS TRANSACTIONS A

of Si film. The phase-field model is a very efficient one, especially in numerical treatment of solidification behavior, because all the governing equations are written in the unified form in both the solid and liquid phases without tracking the interface position. First, we will calculate the stationary S/L interface pattern during stationary heating, and then we will determine the effect of processing variables such as the movement velocity of the radiation heating source and the radiation width on the evolution of the S/L interface pattern during ZMR.

II.

MODEL

Figure 1 shows a schematic diagram of the ZMR process, consisting of an Si film on a substrate and a radiation heater with a radiation-power density profile showing a Gaussian distribution. As proc