Investigation of Thickness Dependence in Crystallization of Thin Films Using Phase Field Modeling

Polycrystalline thin films are widely used in nanoelectronics. Recently, the importance of controlling microstructure keeps growing in the cutting-edge nodes of integrated circuit technology. Two representative examples are the polysilicon channel of 3D NAND and the dielectric film of the DRAM capacitor. In both applications, the grain size is important because grain boundaries act as the resistance for the channel and the leakage path for the dielectric. It has been experimentally observed that thicker films have larger grain size in the case of the polycrystalline film prepared by solid-phase crystallization (SPC), i.e., annealing following depositing an amorphous film. However, the origin of the thickness was unclear.<br/>In this study, the relation between film thickness and grain size was investigated experimentally and theoretically. 10, 20, 40 nm thick poly-germanium films were prepared by the SPC process and their grain sizes were obtained by analyzing images from transmission electron microscope. The results clearly show the thickness dependence of the grain size. We successfully reproduced the experimental trend using phase-field simulation. The densities of heterogeneous and homogeneous nuclei, which are main model parameters, were calibrated to fit the experimental results because they are extremely difficult to measure in such thin films. The thickness dependence of the grain size can be explained by the difference between the growth velocity of 3D and 2D grains with the same radius. The grain size is much smaller than the film thickness in the initial stage of annealing where the grain is three-dimensional. Conversely, the grain size is much larger than the film thickness in the late stage of annealing where the grain is two-dimensional. Thinner films reach the 2D grain stage earlier, implying that the grain growth becomes slower at a smaller grain size. Our results may provide process engineers a good insight and our calibrated model can be utilized in the design of thin film process.