Model of the ALILE Process

The experimentally observed results regarding nucleation and growth are discussed with the help of the phase diagram of the Al/Si system [52-54]. The Al-rich part of the phase diagram is shown in the left part of Fig. 12.12. In the phase diagram the temperature T is shown versus the C si. The equilibrium lines are indicated as solid lines. At the eutectic temperature of the Al/Si system (Teu = 577°C = 850 K), a maximum of about 1.5at.% Si can be dissolved in solid Al. The ALILE process takes place below the eutectic temperature (e.g., at 750K). This means that the transition occurs directly from the (Al) phase to the (Al) + (Si) phase. For the following discussion, three important values of the C si within the Al are defined  

The saturation concentration Cs is the equilibrium concentration of Si in Al at a certain temperature (solubility). When Al is in contact with crystalline Si, there is a flow of Si atoms into the Al as long as the C si within the Al is lower than the Cs. For example, the Cs at 750K is about 0.6at.%. 

The time evolution of the C si within the A1 layer was also calculated to verify the above stated model of the ALILE process [56, 57]. All three experimentally observed stages of the ALILE process were investigated stage I (no nucleation, no growth), stage II (nucleation and growth), and stage 

III (no nucleation, but growth). The results of the calculations are in good agreement with the model discussed above. 

The model is based on the following considerations Due to the fact that 111 planes of crystalline Si feature the lowest specific surface energy these planes are preferentially formed [62,63]. This leads, for example, in the case of solid phase crystallization of a-Si, to a double-pyramid (octahedral) structure 

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